Washington (CNN) -- The District of Columbia's same-sex marriage law will go into effect as scheduled this week, after the Supreme Court refused to stop its enforcement.

Chief Justice John Roberts issued a three-page order Tuesday, a day before the law becomes official. He concluded the high court should defer to local matters in the federal district of Washington. And he said a separate ballot initiative to overturn the law would give voters a chance to weigh in on the question.

A group of Washington residents had objected to the Religious Freedom and Civil Marriage Equality Amendment Act, which expands the definition of marriage to include same-sex couples.

Those opponents had argued city residents should have been given a chance to vote on the high-profile issue before the city council passed the measure. They still seek to force a ballot initiative after the law takes effect. Local courts had turned down various lawsuits to block it.

The district's marriage bureau says same-sex couples can begin applying for marriage licenses Wednesday. However, by law, "three full days must pass between the day of application to the day that the license can be issued," the bureau, part of the district's superior court system, says on its Web site, so no marriages would be held this week.

A $35 application fee is waived for couples who are registered domestic partners, although a $10 fee for the license is not, the bureau said.

District of Columbia Mayor Adrian Fenty signed a measure recognizing same-sex marriages as legal in December, after the city council overwhelming passed it. It then had to go through a review period during which Congress had an opportunity to intervene.

The district joins Connecticut, New Hampshire, Vermont, Massachusetts and Iowa in allowing same-sex couples to marry.